blender 2.8 obj or x3d import texture usage
This is easily done with a material node setup by adding an attribute input node and setting the Name value to Col and plug that into the shader of your choice.  I've used a diffuse BSDF shader here, but you can pipe the color to any node color input you so desire.



You could also this by baking the vertex colors out to a texture.

Please refer to the following question for a how to guide.

Bake vertex colors to texture from mesh